Recent studies on viscous streaming flows in two dimensions have elucidated the impact of body curvature variations resulting flow topology and dynamics, with opportunities for microfluidic applications. Following that, we present here a three-dimensional characterization as function changes geometry topology, starting from well-known case sphere to progressively arrive at toroidal shapes. We l...

The new 3and 4-manifold invariants recently constructed by Ozsváth and Szabó are based on a Floer theory associated with Heegaard diagrams. The following notes try to give an accessible introduction to their work. In the first part we begin by outlining traditional Morse theory, using the Heegaard diagram of a 3-manifold as an example. We then describe Witten’s approach to Morse theory and how ...

In this paper we will survey the the various forms of convexity in symplectic geometry, paying particular attention to applications of convexity in low dimensional topology.

February 3, 1998 Topology Changes in (2+1)-Dimensional Quantum Gravity Yoshihisa FUJIWARA, Saburo HIGUCHI1 , Akio HOSOYA2 , Takashi MISHIMA3 and Masaru SIINO Department of Physics, Tokyo Institute of Technology, Oh-Okayama Meguro-ku, Tokyo 152, Japan ABSTRACT We study topology changing processes in (2+1)-dimensional quantum gravity with negative cosmological constant. By playing the `gluing-man...

In (2+1)-dimensional general relativity, the path integral for a manifold M can be expressed in terms of a topological invariant, the Ray-Singer torsion of a flat bundle over M . For some manifolds, this makes an explicit computation of transition amplitudes possible. In this paper, we evaluate the amplitude for a simple topology-changing process. We show that certain amplitudes for spatial top...